Ab initio screening of quantum frustrated materials with kagome and triangular geometries

Abstract

Geometrical frustration is a powerful route to realize exotic phases such as quantum spin liquids. Despite extensive efforts, systematic searches targeting specific frustration motifs and their potential to host unconventional magnetic ground states remain rare, thus highlighting the need for a more focused and predictive materials discovery approach. Here we present a new strategy combining high-throughput first-principles calculations, magnetic force theory, and spin Hamiltonian analysis. Starting from the 150,000 material database, we catalogue candidate materials that may host competing exchange interactions and new types of magnetic states with the focus on kagome or triangular lattices. Our workflow not only reproduces the majority of known frustrated magnetic materials, validating our approach, but also predicts novel candidate compounds with targeted frustration profiles that have not yet been experimentally synthesized. Among these, we identify six promising new materials: one triangular lattice compound, KMgNiIO6, and five kagome lattice compounds; Li4Fe3WO8, Li2V3F8, Li5VP2(O4F)2, and Li2MgCo3O8 (P2/m and C2/m). For each candidate, we identify detailed magnetic properties and further propose their potential magnetic ground states, revealing that some of them may host entirely new magnetic phases driven by their distinct frustration characteristics.

Figures (9)

• Figure 1: (a) Calculated magnetic moments at TM sites for 1,653 materials yielding stable magnetic solutions. (b) Schematic overview of the multi-step high-throughput screening workflow and the corresponding results. Starting from a database of 154,713 materials, the procedure ultimately provides the catalog of frustrated magnetic materials and identifies the six strongest candidates which have not yet been synthesized. (c) Crystal structures and associated intra-layer exchange interactions for triangular and kagome lattices. (d, e) Calculated $J_{1}$ values and their ratios with respect to the largest inter-layer coupling ($J_{\mathrm{out}}^{\mathrm{max}}$). The yellow-shaded region indicates the screening threshold $|J_{\mathrm{out}}^{\mathrm{max}}|\leq 0.1 J_{1}$ (with AFM $J_1$). Panels (d) and (e) present results for triangular and kagome systems, respectively. By convention, positive (negative) $J$ corresponds to antiferromagnetic (ferromagnetic) interactions.
• Figure 2: Catalog of (a) triangular and (b) kagome lattice compounds situated in the magnetically frustrated regime, plotted in the $J_2/J_1$--$J_3/J_1$ parameter space. Each numbered marker corresponds to a specific material, with yellow circles indicating compounds that have been experimentally synthesized and blue circles representing unsynthesized candidates. The color scale denotes the calculated ordered magnetic moment $m$ (in $\mu_B$). Green lines mark the condition $J_{3(a/d)} = J_2$, and magnified insets highlight regions with dense data distributions.
• Figure 3: Classical ternary phase diagrams for (a) $J_{1}-J_{2}-J_{3d}$ and (b) $J_{1}-J_{2}-J_{3a}$ kagome Heisenberg models. Couplings are normalized such that $J_{1} + J_{2} + J_{3a(3d)} = 1$. The dashed region indicates the parameter regime of the material obtained from the DFT$+U$ calculation. The inset illustrates how to read the ternary phase diagram. (c) Real-space spin configurations for each ordered phase. The spin colors correspond to the spin directions on the cuboctahedron shown on the left.
• Figure 4: (a) Projected density of states (PDOS) for KMgNiIO6 ($P312$). The red and green lines represent the Ni-$3d$ and O-$2p$ states (per atom), respectively. (b) The local atomic structure around transition-metal site (NiO$_6$). (c) Top and (d) side view of the crystal structure. The Ni$^{2+}$ ions in the NiO6 octahedral environment adopt a $t_{2g}^6 e_g^2$ electronic configuration. Each triangular Ni layer is well isolated by non-magnetic K layers, resulting in a quasi-two-dimensional magnetic lattice. The $C_3$ rotational symmetry along the $(001)$ axis and the $C_2$ symmetry along the $(210)$ direction within the triangular plane ensure that all NN exchange couplings ($J_1$) are equivalent. The NN Ni–Ni distance is 5.24Å, and the magnetic superexchange pathway involves two distinct long-range bridges: Ni–O–I–O–Ni and Ni–O–Mg–O–Ni. These extended exchange paths give rise to a weak antiferromagnetic coupling with a small value of $J_1 = 0.079$ meV.
• Figure 5: (a) PDOS for Li5VP2(O4F)2($P3$). The red, green and cyan lines represent the V-$3d$, O-$2p$ and F-$2p$ states (per atom), respectively. (b) The local atomic structure around transition-metal site (VO$_4$F$_2$). (c) Top and (d) side view of the crystal structure. The V^3+ ions, coordinated by O4F2 octahedra, nominally host two valence electrons in $t_{2g}$ orbitals. While $C_3$ rotational symmetry around the $(001)$ axis is preserved, the presence of inter-layer Li ions breaks inversion symmetry, leading to a lowering of the overall lattice symmetry. As a result, the NN magnetic interactions split into two symmetry-inequivalent values, despite the underlying $C_3$ and translational symmetries. Consistent with this expectation, our MFT calculations yield two distinct NN couplings: $J_{1} = 0.035$ and $0.036$ meV. In the Supplementary Table. \ref{['supple_cDFT_mp_758318']}, we report the average of these two values for simplicity. The long interatomic V–V distance of 5.05Å, coupled with extended superexchange pathways (V–O–Li–F–V and V–O–Li–O–V) accounts for the relatively small magnitude of $J_1$.